Yeah, I added a ship upgrade and never even got it beyond halfway full. Granted I don't pick up everything, and I usually sold spare armor/weapons each town visit out of habit, but exotic materials and resources I always grabbed, and ended up with like 1100 mass out of 2600 on my ship.
You can modify your ships without having any of the shipbuilding stuff I think. You are limited, but you can add cargo space with some penalty to range and mass to help ease it that. Additionally, storage via outpost is cheap. It's like 3 iron, 2 aluminum, 2 adaptive frames for 250 mass resource storage. Build a couple of those at an outpost and you're set. If you do a....I don't remember the name, but a storage link between your ship and containers, you can transfer straight from ship to container without taking it out of cargo. Just mass dump things into storage and be cleared out.
Alternatively, if you have a lot of credits, Shieldbreaker, a class B ship at New Atlantis, is a wonderful ship. Like 2300 mass stock, and you can add more if needed with minimal penalty.
It takes 4 minutes to craft like 30 storage containers and the piece to move stuff off your ship easily.
Every single Bethesda game since at least Daggerfall has had carry weight. This isn't a new concept within Bethesda games. If you are hoarding crafting materials, why not...use them to craft things so you can hoard more?
They're always the first mods I installed in skyrim. So many times you get a surprise dragon fight after just clearing out and looting an entire dungeon. I hate killing it and then not being able to pick up the bones because oooh no you're already carrying too much!